Five number summary for grouped data Formula & Example-1

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Five number summary for grouped data Formula & Example-1 ( Enter your problem )

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Formula & Example-1
Example-2
Example-3
Example-4

Other related methods

8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
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2. Example-2
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1. Formula & Example-1

Formula

Five number summary includes five values

1. Minimum value
2. First quartile `Q_1`
3. Median `Q_2`
4. Third quartile `Q_3`
5. Maximum value

Examples
1. Calculate Five number summary from the following grouped data
X Frequency
0 1
1 5
2 10
3 6
4 3

Solution:
Five number summary :

`x`	Frequency `f`	`cf`
0	1	1
1	5	6
2	10	16
3	6	22
4	3	25
---	---	---
	n = 25	--

Minimum value `=0`

Maximum value `=4`

First quartile `Q_1` :

Here, `n = 25`

`Q_1 = ((n+1)/4)^(th)` value of the observation

`=(26/4)^(th)` value of the observation

`=(6.5)^(th)` value of the observation

`=2`

Median `Q_2` :

`Q_2 = ((2(n+1))/4)^(th)` value of the observation

`=((2*26)/4)^(th)` value of the observation

`=(13)^(th)` value of the observation

`=2`

Third quartile `Q_3` :

`Q_3 = ((3(n+1))/4)^(th)` value of the observation

`=((3*26)/4)^(th)` value of the observation

`=(19.5)^(th)` value of the observation

`=3`

Thus Five number summary is
1. Minimum value `=0`

2. First quartile `Q_1=2`

3. Median `Q_2=2`

4. Third quartile `Q_3=3`

5. Maximum value `=4`

This material is intended as a summary. Use your textbook for detail explanation.
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